No current phone has the power needed to be able to play twilight princess also which version of the s4 do you have(i think theres one that does not support opengl), and as always i recommend build 427 from https://dl.dolphin-emu.org/builds/ Just uninstall your current version and install that one.

getting a gamecube isn't a bad idea as it will work no problem, if you have a wii and gamecube controller you can play it there too but the advantage of the computer is you can upscale the resolution and play it at full hd as long as you have a powerful cpu and gpu